In a design process of a conveying path, examination of functions of a product to be designed under various conditions before production of an actual product can reduce the number of steps required to manufacture and test a prototype, and can reduce the development period and cost. In order to simulate the behavior of a paper sheet in a conveying path for such purpose, an equation of motion that describes the motion of a flexible, sheet-like printing medium (to be referred to as a flexible medium hereinafter) such as a paper sheet, film, or the like, which is conveyed in a conveying path of a copying machine, printer, or the like must be solved. Note that the printer includes an LBP (laser beam printer), ink-jet printer, and the like. In order to solve this equation of motion, a space and time must be algebraically approximated as finite quantities, and their simultaneous equations must be solved. In order to algebraically approximate a space, a finite element method, difference method, and the like are known (for example, see Japanese Patent Laid-Open Nos. 11-195052 and 11-116113).
In order to solve the motion of a flexible medium, as described above, the equation of motion of the flexible medium which is discretely expressed by finite elements or mass-spring system is formulated first. Next, an analysis target time period is divided into time steps each having a finite width, and the motion of the flexible medium is solved by numerical time integration that sequentially calculates the acceleration, velocity, and deviation as unknown quantities for each time step from time 0. As the method of solving the motion of a flexible medium, the Newmark β method, Wilson θ method, Euler's method, Kutta-merson method, and the like are well known. In order to precisely simulate the convey state of a medium, element divisions of the medium and time step intervals must be set very finely. Also, a problem of, e.g., a false slip caused between the roller and medium when an unexpected external force acts during conveyance of the flexible medium must be solved. In order to solve these problems, the peripheral velocity, roller radius, and center distance of a convey roller pair are input, and the convey roller surface is divided into a pressure contact area and non-pressure contact area on the basis of the input information. Next, when a flexible medium reaches the non-pressure contact area of the convey roller pair, a convey force is applied to the flexible medium in accordance with the difference between the peripheral velocity of the non-pressure contact area and the moving velocity of the flexible medium. Also, as is well known, when the flexible medium reaches the pressure contact area of the convey roller pair, it is designed to forcibly convey the flexible medium at the peripheral velocity of the roller pair (e.g., see Japanese Patent Laid-Open No. 2004-189436).
In the aforementioned design support apparatus, when the behavior of a flexible medium in the conveying path, i.e., the convey process of the flexible medium, guide resistance, and the like, are to be accurately evaluated, the contact state of the flexible medium and convey rollers and, more particularly, a nip shape and the angles of the flexible medium at the entry and exit sides of the nip, must be accurately expressed. In the following description, the nip will be defined as a contact area of the convey roller pair.
For example, in the convey roller pair generally used in the conveying path, one convey roller uses a roller prepared by winding a flexible material with a high coefficient of friction such as rubber or the like around a core member with a high rigidity such as iron, aluminum, or the like. When this roller with the flexible surface is used, the other roller uses a roller made up of a material with a high rigidity such as iron, aluminum, or the like, and a combination of the flexible and rigid rollers are often used. Even when both the convey rollers are rubber rollers, they may have different degrees of hardness or thicknesses of rubber. For this reason, when these convey roller pair contact each other, the nip has a shape which is compressed from the high rigidity side toward the low rigidity side in place of a flat shape, and the flexible medium clamped there follows this shape. Furthermore, the angles of the flexible medium at the entrance and exit of the nip are inclined toward the rigid roller side due to the nip shape. In order to correctly calculate the behavior of a paper sheet such as the contact position, contact angle, and the like between the paper sheet and guides upon conveyance, these factors around the nip must be taken into consideration.
However, in the aforementioned design support apparatus, the nip shape formed by a contact between the flexible medium expressed as a manifold of the masses and springs and convey roller pairs does not consider any deformation difference due to the rigidity difference of the convey rollers in the convey roller pair. For this reason, as the nip shape, a method of defining a line segment that connects intersections of the convey rollers as the nip is adopted. Also, a method of defining the entry and exit angles of the flexible medium with respect to the nip in the same direction as this line segment or designating them as vectors or the like by the user is adopted. For this reason, the conventional design support apparatus which does not consider any nip shape or the like formed by a contact between the flexible medium and convey roller pair cannot often accurately evaluate an actual behavior (convey process) of the flexible medium.
On the other hand, in the aforementioned design support apparatus, it is a common practice to input the control of the convey rollers as a chart that represents the drive conditions. This chart uses values which are theoretically estimated from control conditions given by design, motor performance, and the like, values obtained by actually measuring the motions of the convey rollers, or the like.
However, in numerical calculations required to solve the motion of the flexible medium, calculations are implemented by mechanically dividing an analysis target time period into time steps each having a finite width. At this time, calculation steps do not always match feature points in the drive chart such as drive start and end times of the convey rollers, drive velocity change times, and the like. In the following description, the drive start and end times of the convey rollers or the drive velocity change times in the drive chart will be referred to as feature points. As a result, upon adjustment of calculation conditions for respective steps, the drive conditions such as the drive start and end times and the like may become different from values designated by the drive chart. Of the drive conditions of an actual device, driving may be invoked depending on a given condition during the operation such as the position of the flexible medium or the like. In this case as well, the feature points of the chart may not match the actual calculation step times.
In such case, if a person who uses this design support apparatus is the designer of this apparatus or the one who recognizes details of calculation steps, he or she can take appropriate action by evaluating whether or not the analysis result is affected by them. This is because the designer or the like recognizes problems and points to keep in mind of a numerical simulation when the calculation steps do not match the feature points in the drive chart. However, when the person who uses this design support apparatus is a general user, he or she can hardly evaluate whether or not the calculation result is affected by the aforementioned problems, and cannot determine appropriate time discretization.
As is also known, in order to accurately evaluate the behavior of the flexible medium in the conveying path by the aforementioned design support apparatus, a variation rate of the convey velocity with reference to a nominal value is calculated using the contact structure analysis scheme using a finite element model. The variation rate of the convey velocity with reference to the nominal value is produced when an elastic member 1002 such as rubber or the like which forms a roller 1001 deforms under pressure. With this method, the roller 1101 is pressed by a rigid roller 1003 by compression, and the surface of the roller 1001 deforms along the surface shape of the rigid roller 1003, as shown in FIG. 15. Note that the rollers 1001 and 1003 form a convey roller pair. The roller 1003 is a rigid roller formed of a high-rigidity material such as iron or the like, and the roller 1001 is a roller on a core surface of which a layer 1002 of a flexible material such as rubber or the like is formed. A flexible medium 1004 such as a paper sheet or the like is clamped and conveyed between the roller 1001 and rigid roller 1003. A portion where the two rollers contact the paper sheet and receive a pressure is a nip 1011. The flexible medium is conveyed while being in tight contact with the nip between the rollers. When the roller rotates by Δφ, as shown in FIG. 16, a moving amount of the circumference of the roller 1001 at a position which is far from the nip and free from any deformation is R×Δφ (R is the radius of the roller), as indicated by a vector 1012. However, since the roller surface in the nip 1011 is stretched in the circumferential direction due to deformation, as shown in FIG. 15, the moving amount of the roller surface is larger than that given by the above formula accordingly. The convey amount of the flexible medium in the nip 1011 is represented by a vector 1013. For this reason, the convey velocity in the nip 1011 becomes higher in correspondence with the stretch of the roller in the nip. This velocity variation rate changes depending on parameters such as the thickness, hardness, pressure, and the like of rubber.
As described above, a velocity at which the rollers convey the flexible medium is not uniquely determined based on the roller radius and rotational speed. In actual design, the roller convey velocity does not normally have a designed value, and suffers variations.
As one factor of convey velocity variations, an elastic member such as rubber or the like which forms the roller deforms, and the length of the circumference changes. This amount is determined by the material and hardness of the roller, the thickness of the rubber layer, that of the surface layer, the pressure, and the like, and it is essentially difficult to introduce specific numerical values from a simple formula.
There is a demand to implement behavior simulations of the tension, slack, and the like produced on the flexible medium with higher accuracy by estimating the effects of such velocity variations.